I have both put directly into soil and done the paper towel method both with success. I usually put them on a plate, and invert another plate on top. They sprout in a couple days...then I plant in soil.
I've had seeds for a couple years that grew...and then again I ordered some seeds that would almost REFUSE to grow and they were only 3 months old. So, one factor is the quality or type of seed.
These are probably some kind of sucking pest that is chomping on your leaves. I had a very similar problem and it looks like I found a solution.
My leaves were showing the exact same signs as yours (judging from the pics). Also I was seeing the tips turing brown and curling up, and also weird...